a. Write the first four rows of Pascal’s triangle. b. Expand (a + b)3

Q: Prove: | a | - | b | <= | a + b |

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Q: The sum of the entries in row 10 of Pascal's Triangle is: O 211 O 102 210 10 acer

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Q: Expand the following using the pascal's triangle 1. (5+ 2d)3

A: We will use the pascal's triangle to expand the given expression.

Q: 4. Determine the binomial coefficients in the 4th row of Pascal's triangle and use them to expand 3x…

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Q: A secant segment consists of an external secant segment and an internal secant segment. O True O…

A: The given statement is: The secant segment consists of an external secant segment and an internal…

Q: Express 50 C30 as a sum of two terms from Pascal's triangle, each in the form Cr. O 51 C30 +51 C31 O…

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Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

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Q: 2. Find the missing numbers in the magic square below. 2 13 10 11 6. 12 15 1 4-

A: Consider the provided table,

Q: 15. What is the sum of the 11th row of Pascal's triangle? a. 2048 b. 1024 C. 976 d. 2056

A: Pascal's Triangle is a method to know the binomial coefficients of terms of binomial expression (x +…

Q: E Show that the sum of the squares of the first n Fibonacci numbers is given by the formula u + už +…

A: I have proved the result by using given hint

Q: What are the first 5 entries in row 100 of Pascal's Triangle? O 100 C1, 100 C2, 100 C3, 100 C4, 100…

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Q: Find the first five O Written compact n 13

A: Introduction: The formula for the Taylor series from the function y=f(x) centered at x=a is given…

Q: 58. a. Write the first four rows of Pascal's triangle. b. Expand (a + b).

A: The pascal's triangle is a type of a triangular array which is constructed in such a way in which…

Q: 2) Find the o - Congugates ot; c) 5

A: 2. To Find: θ-conjugates of  (c) 54 (d) 1+2

Q: What Role do proofs play in mathematics?

A: Given: The objective is to explain the role of proofs in mathematics.

Q: 63 6O 216 O True ||

A: Given Data: Equation: 6360=216 The value of any number raised to 0 is 1. So 60=1. The value of six…

Q: a) If P(A)=1/3 and P(B)=3/5 and, A and B are mutually exclusive then P(A or B') = 14/5. Is it true…

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Q: How do you create Pascal's Triangle?

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Q: a) What is the sum of all the entries of row 12 of Pascal's triangle? b) What is the sum of all the…

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Q: Find a counterexample to show that the following statement is false. The sum of two four-digit…

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Q: 1. Find a counterexample to show that each statement is false: The sum of three multiples of 5 will…

A: Counterexample is to show the statement false by proving some example is wrong with the statement.…

Q: Use Pascal's Triangle and comblnations to expand and simplify each of the following: a) (a+b) b) (x-…

A: Given: a)  (a+b)7b)  (x−3)5

Q: For a set of three objects, find the number of different subsets of size 2. (Use row 3 of Pascal's…

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Q: - How many secret codes can be formed consisting of five letters or four digits (but not both), if…

A: If the code has 5 letters.Then we can select each letter in 26 ways. So we can select 5 letters in…

Q: 5.Find the product of the first five terms of a GP, if its third term is 4.

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Q: Find the sum of the coefficients of (a+2b)⁶. Using pascal triangle

A: This question is related to binomial distribution.

Q: "he row of Pascal's Triangle that corresponds to n = 8 is as follows: 1 8 28 56 70 56 28 8 1. What…

A: Given data,

Q: 3a + 6ab = 18ab² What is a?

A: see below the answer

Q: How would you use Pascal's Triangle to expand (x +y)^6

A: The row form of the Pascal's triangle starting 1, 6, 15 ... gives the sequence of coefficients for…

Q: Use Pascal's Triangle to expand (5 + 2y)*.

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Q: Find the formula for the nth term of the arithmetic sequ 3, 6, 9, ... an ||

A: Given arithmetic sequence is The first term of the sequence is a=3  and common difference is…

Q: What is the row of Pascal's triangle containing the binomial coefficients (), 0 < k < 9?

A: The first row of pascal triangle contains only one element i.e. 1. In second row, there are two…

Q: A box with a square base and no top is to be made from a square piece of cardboard by cutting 2 in.…

A: Let consider that x be the length of one side of the cardboard When 2 inches are removed from each…

Q: If a 3 are ordinals and a C 3, then a € 3.

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Q: Expand and simplify using Pascal's Triangle (3x² - y)5

A: In this question, we need to find the expansion of (3x2-y)5 using Pascal's triangle.

Q: 1. What is the sum of the first 7 terms in diagonal 10 of the Pascal's Triangle? 2. What is the sum…

A: We have to give the answer related to pascal triangle.

Q: 3) The sum of the terms in the 9th row in Pascal's Triangle is

A: Step-by-step solution Step 1 of 3 The Pascal’s triangle is shown below:

Q: 2 6. The sum of the first n odd natural numbers is equal to n.

A:

Q: 5. What would go in the justification column for line (7) of this proof: (4) (5) 2,3 (6) 1,2,3 (7)…

A: Since you have posted a multiple  question according to guildlines I will solve first   question…

Q: 4. Find The Three cube Meots of 1

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Q: 36 7 6 9 4 10 8 3 7 5 85 9 4 10 33 7 5 6. 3.

A: For a magic square, Sum of row elements = Sum of column elements = Sum of diagonal elements   a) In…

Q: 11. The row of Pascal's triangle that corresponds to n = 8 is as follows: 1 8 28 56 70 56 28 8 1.…

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Q: 3. The row of Pascal's Triangle that corresponds to n = 8 is as follows: 1 8 28 56 70 56 28 8 1.…

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Q: Expand the following binomial powers using Pascal's Triangle 1. (3x-2y)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: What is 40 Cb+ 40 C6+1 expressed as a single term in the form n Cr in Pascal's Triangle? O 80 C2b+1…

A: Solution:-

Q: 10 4 %3D 1 10,000 O True O False

A: We have given expression as   104=110000   we have to tell whether it is true or false

Q: Do u know how to do this

A: In B each side of the each red triangle = 1/2 units So perimeter of one red triangle= 3*1/2= 3/2And…

Q: Prove (without expansion) a b c d |-b -d d -b = (a? + b? + c? + d?)? a a |-d -c b a

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Q: What is the sum of the first 7 terms in diagonal 10 of the Pascal’s triangle?

A: Given :   Pascal's triangle